This invention relates to an apparatus for measuring the spatial average of a physical property of a substance using radiation, the term "radiation" being here used to refer to all forms of electromagnetic radiation including X-rays, gamma rays, and visible light. More particularly but not exclusively, it relates to a component analyzer for determining the proportions of the components in a multi-component fluid flowing through a pipe.
FIG. 1 is a schematic diagram of a conventional measuring apparatus in the form of a component analyzer which employs radiation to analyze the components of a fluid within a pipe. In the figure, element number 1 is a radiation source which produces X-rays or gamma rays, element number 2 is the radiation which is emitted from the radiation source 1, element number 3 is a pipe which is irradiated with this radiation 2, element number 4 is a two-component fluid to be measured which is flowing through the pipe 3, element number 5 is a collimator which is disposed on the opposite side of the pipe 3 from the radiation source 1, element number 6 is a through hole which is formed in the collimator 5 and through which radiation can pass, element number 7 is a radiation detector which detects the radiation 2 which passes through the through hole 6, and element number 8 is a signal processing and calculating device which processes the signal from the radiation detector 7 and outputs a signal corresponding to some physical property of the fluid 3 being measured.
The attenuation of radiation such as X-rays or gamma rays passing through a substance is expressed by the following equation. EQU I=I.sub.o exp (-.mu..rho.t) (1)
wherein Io is the intensity of the incident radiation, .mu. is the absorption coefficient with respect to radiation of the substance through which the radiation is passing, .rho. is the specific gravity of the substance, t is the thickness of the substance through which the radiation passes, and I is the intensity of the radiation after passing through the thickness t. When the fluid 4 of FIG. 1 comprises a first substance and a second substance and the specific gravities thereof are respectively .rho..sub.1 and .rho..sub.2, the mass absorption coefficients with respect to the radiation are respectively .mu..sub.1 and .mu..sub.2, the thicknesses of the first and second substances through which the radiation passes are respectively t1 and t2, and the length of the path along which the radiation passes where the thicknesses are measured is L, then the following relationships hold. EQU .mu..sub.1 .rho..sub.1 t.sub.1 +.mu..sub.2 .rho..sub.2 t.sub.2 =ln (I.sub.o /I)-a (2) EQU t.sub.1 +t.sub.2 =L (3)
a is a constant which is determined by the material, the thickness, and other characteristics of the pipe 3. The other values .mu..sub.1 .multidot..mu..sub.2 .multidot..rho..sub.1 .multidot..rho..sub.2 .multidot.Io, and L are known in advance. Therefore, when the proportion of the two components is not known, if the intensity I of radiation after passing through the fluid is measured, the values of t1 and t2 can be found from Equations (2) and (3), and the proportion of the components along the pathway of the radiation can be determined.
In FIG. 1, radiation 2 is emitted from the radiation source 1, it passes through the walls of the pipe 3, the fluid 4 being measured, and the through hole 6 of the collimator 5 and enters the radiation detector 7. Signals from the radiation detector 7 are sent to the signal processing and calculating device 8. Here, t1 and t2 are determined based on Equations (2) and (3), and component analysis along the path of the radiation 2 is performed. The distribution of the two components in the pipe 3 is not necessarily uniform. Therefore, the collimator 5 is successively moved by an unillustrated drive apparatus to a number of different positions to change the location of the through hole 6, and measurement is performed in the same manner at each location. By taking measurements at n different locations, i.e., by measuring the component proportions along n different paths of radiation, and by taking the average of the measurements, an average value of the proportions of the components in a cross section of the fluid 4 is obtained. This average is calculated by the signal processing and calculating device 8.
Equation (2) can also be written as follows. EQU .mu..sub.1 .rho..sub.1 t.sub.1 +.mu..sub.2 .rho..sub.2 t.sub.2 =-ln (I)+C (4)
If each of the n radiation pathways is distinguished by a subscript i and summations are performed for the n pathways, then the following equations, which correspond to Equations (2) and (3), can be written. ##EQU1##
The average value of the proportions of components 1 and 2 for all the pathways can be found by determining the value of ##EQU2## and ##EQU3## so it is only necessary to determine ##EQU4## and it is not required to find the individual values of ln (I.sub.i) or I.sub.i. Namely, the average value of the component proportions over a cross section can be found by determining the sum of the logarithms of a quantity related to the radiation 2, i.e., the intensity I of the radiation after passing along each of the n pathways.
The radiation 2 is a type of quantum, and therefore the output signal from the radiation detector 7 signal exhibits a constant statistical fluctuation. The measurement error due to this fluctuation decreases in inverse proportion to the square root of the measurement time if the intensity of the radiation 2 is constant. Therefore, in order to perform highly accurate measurement, a long measurement time is necessary. Furthermore, if the through hole 6 of the collimator 5 is successively moved to n different location and n separate measurements of radiation are made, the time required for measurement becomes roughly n times that required for measurement of a single pathway. Therefore, highly accurate measurement requires a very long time.